Question

Professor Smith and Professor Jones are going to produce a new introductory textbook. As true scientists, they have laid out the production function for the book as q=S1/2J1/2q=S1/2J1/2, where q = the number of pages in the finished book, S = the number of working hours spent by Smith, and J = the number of hours spent working by Jones. After having spent 900 hours preparing the first draft, time that he valued at $3 per working hour, Smith has to move on to other things and cannot contribute any more to the book. Jones, whose labor is valued at $12 per working hour, will revise Smith's draft to complete the book.a. How many hours will Jones have to spend to produce a finished book of 150 pages? b. What is the marginal cost of the 150th page of the finished book? Of the 300th page?

Answer 1

Answer:

(a) It will take Jones 25 hours to produce a finished book of 150 pages

(b) The marginal cost of the 150th page of the finished book is $4

The marginal cost of the 300th page of the finished book is $8

Explanation:

q=$S^{1/2}$$J^{1/2}$ = $\sqrt{SJ}$

q = the number of pages in the finished book

S = the number of working hours spent by Smith

J = the number of hours spent working by Jones.

For first draft, smith works for 900 hours at $3 per working hour

q = $\sqrt{900J}$

q=$\sqrt{900}$ × $\sqrt{J}$

q = 30 × $\sqrt{J}$

$\frac{q}{30}$ = $\sqrt{J}$, squaring both sides we have,

($\frac{q}{30}$)² = J

(a) Since Jones has to produce a book of 150 pages and Smith worked 900 hours on it,

q = 150, S = 900 , J = ?

J = ($\frac{150}{30}$)² = 5²

J = 25

Therefore, it would take 25 hours for Jones to produce a book of 150 pages.

(b) ($\frac{q}{30}$)² = J

Since Smith worked for 900 hours at $3 per working hour, his total cost of work is = 900 × $3 = $2,700.

Jones total cost of work  at $12 per working hour = $12J

Total cost of work, C = $2,700 + $12J

C = $2,700 + $12($\frac{q}{30}$)²

Marginal cost, MC = $\frac{dC}{dq}$

= $\frac{d}{dq}$ [$2,700 + $12($\frac{q}{30}$)²]

= $\frac{4q}{150}$

if q = 150, MC = $\frac{4*150}{150}$

= $4

if q = 300, MC = $\frac{4*300}{150}$ = $8